three-body recombination at vanishing scattering lengths in ultracold atoms
DESCRIPTION
Three-body recombination at vanishing scattering lengths in ultracold atoms. Lev Khaykovich Physics Department, Bar- Ilan University, 52900 Ramat Gan , Israel. Critical Stability workshop, Santos Brasil 10/14/2014. System: dilute gas of ultracold atoms. - PowerPoint PPT PresentationTRANSCRIPT
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Three-body recombination at
vanishing scattering lengths
in ultracold atoms Lev Khaykovich
Physics Department, Bar-Ilan University, 52900 Ramat Gan, Israel
Critical Stability workshop, Santos Brasil 10/14/2014
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System: dilute gas of ultracold atoms
Ultrahigh vacuum environment
Dissipative trapN ~ 5x108 atoms
n ~ 1010 atoms/cm3
T ~ 300 mK
Close to the resonance (orbital electronic states) visible (laser) light – 671 nm (~2 eV)
Magnetic fields
Magneto-optical trap of Li atoms
Dilute gas of atoms:
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Experimental setup: ultracold 7Li atoms
Zeemanslower
MOT~109 atoms
CMOT~5x108 atoms
(300 mK)
~2x104 atoms~1.5 mK
Crossed-beam optical trap
Trapping: conservative atom trap(our case: focus of a powerful infrared laser)
Temperature: ~ mK
Typical numbers:
Relative velocities: few cm/sec
Collision energies: few peV
N. Gross and L. Khaykovich, PRA 77, 023604 (2008)
Evaporation:
Cooling:
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Study of Efimov scenario with ultracold atoms
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Efimov scenario – universality window
01 r
k
1a 01 r
lowest level
first excited level
17.22 17.22
17.22
Borromean region:trimers without pairwise binding
01 2exp sEE n
TnT
00 ln rasN
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Efimov scenario and real molecules
Vbg(R)
Ene
rgy
Atomic separation R
Vbg(R)
En
erg
y
Atomic separation R
No 2-body bound states
One 2-body bound state
Real molecules:many deeply bound states
Vbg(R)
Ene
rgy
Atomic separation R
a < 0 a > 0
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Three-body recombination
Eb/32Eb/3
Release of the binding energy causes loss of atoms from a finite depth trapwhich probes 3-body physics.
Three body inelastic collisions result in a weakly (or deeply) bound molecule.
NnKN 233 K3 – 3-body loss rate coefficient [cm6/sec]
Loss rate from a trap:
U0
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Experimental observables
01 r
k
1a *1 a a1 01 r
Experimental observable - enhanced three-body recombination.
One atom and a dimer couple to an Efimov trimer Three atoms couple
to an Efimov trimer
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Experimental observables
01 r
k
1a a1 01 ra*0
1
Experimental observable – recombination minimum.
Two paths for the 3- body recombination
towards weakly bound state interfere
destructively.
Three atoms coupleto an Efimov trimer
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Experimental observables
B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999).
41
33 )(3
=
aC
mKRecombination length:
Efimov resonance
Recombinationminimum
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Efimov scenario: a short overview Efimov physics (and beyond) with ultracold atoms:
2006 - … 133Cs Innsbruck
2008 – 2010 6Li 3-component Fermi gas in Heidelberg, Penn State and Tokyo Universities
2009; 2013 39K in Florence, Italy
2009 41K - 87Rb in Florence, Italy
2009; 2013 7Li in Rice University, Huston, TX
2009 - … 7Li in BIU, Israel
2012 - … 85Rb and 40K - 87Rb JILA, Boulder, CO
2014 - 133Cs - 6Li in Chicago and Heidelberg* Universities
*Eva Kuhnle’s talk on Friday.
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Experimental playground - 7Li
Absolute ground state
Next to the lowest Zeeman state
3 identical bosons on a single nuclear-spin state.
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Experimental playground - 7Li
Feshbachresonance
Feshbachresonance
Absolute ground state The one but lowest Zeeman state
N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011).
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Experimental results - 7Lia > 0: T= 2 – 3 mK
a < 0: T= 1 – 2 mK
mf = 1; Feshbach resonance ~738G.mf = 0; Feshbach resonance ~894G.
N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).
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Three body recombination at vanishing scattering lengths
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Motivation Purely academic.
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Motivation Purely academic. Application: optimization of evaporative cooling in an
optical trap.
Evaporative cooling in a nutshell:
- high energy atoms are evaporated due to final potential depth;
- elastic collisions re-establish the thermal equilibrium;
- Good collisions: elastic;
- Bad collisions: three-body recombination (heating);
- optical trap weakens during evaporation;
which can be compensated by increasing a.
But:
nel
423
23 anKnb
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Zero-crossings 7Li lower hyperfine level.
Feshbach resonance mF =0 state.
0 200 400 600 800 1000-400
-300
-200
-100
0
100
200
300
400
a [a
0]
Magnetic field [G]
850 G
575 G
412 G
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Early observations
Same scattering length – different three-body recombination rates.
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Early observations
43 aK
Universal region.
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Early observations
N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
Saturation of the three-body recombination rate.
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Two-Body Physics
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Scattering phase shift at zero-crossing
2)(2
1+
)(
1cot kBR
Bakk e
Effective range expansion of the scattering phase shift:
Inconvenient when
0a
22 )(2
1+
tankaRa
k
ke
22aRV ee Effective volume:
See also: C. L. Blackley, P. S. Julienne and J. M. Hutson, PRA 89, 042701 (2014).
Inverted expression:
Well defined when
0a
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Feshbach resonances and zero-crossings
800 820 840 860 880 900 920 940
-400
-200
0
200
400
Magnetic field [G]
Scattering length and effective range:
N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
500 550 600 650 700 750 800-10
0
10
20
30
40
a, R
e [a
0]
Magnetic field [G]
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Two-body physics near zero-crossingEnergy dependent two-body collisional
cross-section:
222
222
2+1
8sin
8)(
kakV
akVk
kk
e
e
0)( k 2= kVa e 2
2=
kRa
e
Condition for vanishing collisional cross-section:
The zero-crossing position is well defined now by precise characterizationof Feshbach resonances:N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011).P. S. Julienne and J. M. Hutson, Phys. Rev. A 89 052715 (2014) (Data from Heidelberg, ENS, Rice and Bar Ilan).
Experimental approach to test the temperature dependence of the cross-section – evaporative cooling around zero-crossing.
S. Jochim et. al. , Phys. Rev. Lett. 89 273202 (2002). K. O’Hara et. al. , Phys. Rev. A 66 041401(R) (2002).
Zero-crossing of 6Li resonance.
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Evaporative cooling near zero-crossing
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Zero-crossing is at 849.9GMaximum is at 850.5G
Evaporation during 500 msInitial temperature: 31 mK
Two-body collisions show energy dependence.
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Three-body physics near zero-crossing
43 )(3= a
maCK
Universal limit:
Recombination length:
41
max
3
3=
C
mKLm
We measure K3 and represent the results as Lm.
B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999).
4max3 3= mL
mCK
Formal definition:
The universal limit maximal value(*):
54.7=maxC
(*) N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
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Three-body physics near zero-crossing
850 860 870 880 8900
100
200
300
400
500
600
Rec
ombi
natio
n le
ngth
, a
[a0]
Magnetic field [G]
Three-body recombination length:
0
41
26
0 5.3216
amC
r
Van der Waals length:
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Effective recombination length
41
max
3
3=
C
mKLmMeasured recombination
length:
31231
2==
aRVL e
ee
From the effective range expansion the leading term is proportional tothe effective volume.
Effective recombination length:
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
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Three-body physics near zero-crossing
Black: T=2.5 mKRed: T=10 mK
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Three-body recombination shows no energy dependence.
Rules out other possibilities to construct Le such as(in analogy to two-body collisions)
2= kVL ee
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Three-body physics near zero-crossings
Low field zero-crossing.
Prediction for the recombination length in the resonances’ region.
B [G]
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Experimental resolution limit is 100 a0.
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Optimization of evaporative cooling
Scattering length compensation of the density decrease.
Bad/Good collisions ratio:
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Phase space density
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Conclusions Zero-crossing does not correspond to the minimum in 3-
body recombination rates. Three-body recombination rate is different at different
zero-crossings. We suggest a new lengthscale to describe the 3-body
recombination rates. Energy independent 3-body recombination rate. We predict a minimum in 3-body recombination in the
non-universal regime.
The question is how general the effective length is?
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People
Eindhoven University ofTechnology, The Netherlands
Servaas Kokkelmans
Bar-Ilan University, Israel
Zav Shotan, Olga Machtey